Algebra
Algebra Core Concepts
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Understanding Basic Algebraic Expressions: Know how to read, interpret and simplify basic algebraic expressions. Always remember that letters are used to represent unknown numbers.
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Solving Equations and Inequalities: You must be capable of solving both simple linear equations, such as x + 7 = 12, and quadratic equations, where the highest power of the variable is 2.
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Factorising Algebraic Expressions: Be comfortable factorising expressions. It can be simple monic quadratics such as x² + 5x + 6 or harder non-monic quadratics such as 6x² + 11x + 3.
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Rearrangement and Substitution: Know how to rearrange equations to isolate a chosen variable and how to substitute one equation into another. This is crucial for solving simultaneous equations.
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Algebraic Fractions: Understand how to simplify algebraic fractions by factorising and cancelling down. Also, learn to add, subtract, divide and multiply these fractions.
Functions and Graphs
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Understanding Functions: Familiarise yourself with the interpretation and manipulation of functions, including square, cube, exponential and reciprocal functions.
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Plotting Graphs and Shape familiarity: Know how to plot the graph of a function, interpret a graph and familiarise yourself with the shape of quadratic, cubic and reciprocal graphs since these often appear in tests.
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Solving Graphically: Be able to find solutions to equations by considering where graphs intersect. Such solutions typically involve solving simultaneous equations.
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Transforming Graphs: Develop a solid understanding of how graphs transform: know the effects of adding, subtracting, multiplying or dividing a function by a constant.
Advanced Algebra
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Algebra of Polynomials: Learn to add, subtract, multiply and divide polynomials, and become familiar with polynomial long division.
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Solving Quadratic Equations: Know how to solve quadratic equations using three methods: factorising, completing the square, and quadratic formula.
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The Discriminant and Nature of Roots: Understand the discriminant (the part of the quadratic formula under the square root) and how it affects the number and type of solutions of the equation.
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Solving Algebraic Fractions and Equations: Gain proficiency in solving complex equations involving algebraic fractions.
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Handling Exponents and Roots: Become conversant with the rules of indices and how to manipulate expressions involving powers and roots.
Remember that practise is key in developing algebra skills. Stay consistent in your revision and keep practising a variety of problems.